Home
Class 12
MATHS
Show that the function defined by f(x) =...

Show that the function defined by `f(x) = | cos x |` is a continuous function.

Text Solution

AI Generated Solution

To show that the function defined by \( f(x) = |\cos x| \) is continuous, we can follow these steps: ### Step 1: Identify the Functions Involved We can express the function \( f(x) \) as a composition of two functions: - Let \( g(x) = |x| \) (the absolute value function) - Let \( h(x) = \cos x \) (the cosine function) Thus, we can write: ...
Promotional Banner

Similar Questions

Explore conceptually related problems

Prove that the function defined by f(x) = t a n x is a continuous function.

Show that the function defined by f(x) = sin(x^2) is a continuous function.

Show that the function defined by f(x)=cos(x^2) is a continuous function.

Is the function defined by f(x) = |x| , a continuous function?

Show that the function f defined by f(x)=|1-x+|x|| is everywhere continuous.

Show that the function f: Z->Z defined by f(x)=x^2 for all x in Z , is a function but not bijective function.

Show that the function f(x) = |sinx+cosx| is continuous at x = pi .

Show that the function f defined as follows f(x)={3x-2, 0 2 is continuous at x=2 , but not differentiable thereat.

Is the function defined by f(x)=x^2-sinx+5 continuous at x=pi ?

Show that the function f : R rarr R defined by f(x) = cos (5x+3) is neither one-one not onto.